Solving systems of linear equations

CHAPTER 7

• Get 7.1B and a piece of graph paper

• Get out 6.4 so I can check it for group points.

• Copy the below information onto a sheet of paper.

Entry Task 02/17/2011

Section 7.1

• Objective: Solve systems of linear equations by graphing. Model a real life problem using a linear system.

Entry Task 02/12/2013Write the following vocabulary in your math

notebook• A system of linear equations in two variables is two

linear equations with two variables.

• A solution of a system of linear equations in two variables is an ordered pair (x,y) that satisfies each equation in the system.

• If the two lines do not cross (parallel) then there is no solution.

• If the two lines do cross there is one solution.• If the two lines are the same the answer is all real

numbers {(x,y); } RyandRx __

• 1.) Solve each equation for y• 2.) Graph each equation (use a ruler!)• 3.) Find the point of intersection• This is your solution

4.) Check your answer

Et 02/05/2013 copy this down: Solving systems of two linear Equations by graphing

• If the two lines do not cross (parallel) then there is no solution.

• If the two lines do cross there is one solution.• If the two lines are the same the answer is all real

numbers {(x,y); } RyandRx __

• Step 1: make sure all of your variables are lined up

• Step 2: make sure a variable will cancel out if you add the equations; if not multiply

• Step 3: add the two equations• Step 4: Solve for the remaining variable• Step 5: find the other variable• Step 6: write your answer in the form (x,y)

Solving a system of linear equations by elimination

Example

•Solve the linear system. { 1 yx

22 yx

Section 7.2

• Objective: Use substitution to solve a linear system. Model a real life problem using a linear system.

Solving a linear system by substitution

• Step 1: solve one of the equations for one of its variables.

• Step 2: substitute the expression from step one into the other equation and solve for the other variable.

• Step 3: Substitute the value from step 2 into the revised equation from step one and solve.

• Step 4: check the solution in each of the original equations.

Example

•Solve the linear system. {

• Step 1: solve for y in equation 1.

• Step 2: Substitute for y in equation 2 and solve for x.

1 yx22 yx

1xy

1x

1 yxx x

22 yx2)1(2 xx213 x1x

Example cont.• Step 3: to find the value of y, substitute -1 for x in

the revised Equation 1.

• Step 4: check that (-1,0) is a solution by substituting -1 for x and 0 for y in each of the original equations.

• The solution is (-1,0)

1xy11y

0y

• Get out 7.2B so I can check it for group points.

• Solve the following system of equations using substitution, if you need help look on page 405 in your book.

{

Entry Task 02/24/2011

102 yx03 yx

• Get out 7.2B so I can check it for group points.

• Complete 7.2 Standardized Test Practice problems 1-7. You have 14 minutes.

• When finished get a book and worksheet 7.3B and take notes for section 7.3 on the back of the worksheet. 7.3B is due on Tuesday.

Entry Task 02/25/2011

Entry Task 02/28/2011

• Get out 7.3B and prepare any questions you may have.

• If you have no questions start working on problems 1-12, and 19-25

• 13-18 will be extra credit.

Entry Task 03/01/2011

• Get out 7.3B to check for group points

• Do numbers 1 and 2 on 7.3 stp

• Get a book and open to page 360, start taking notes.

Entry Task 03/02/2011

• Get out pg. 363 #1-6 to check for group points

• Get a book and on your homework paper, do problem number 7 on pg. 363.

Section 7.6

• Objective: Solve a system of linear inequalities by graphing. Use a system of linear inequalities to model a real-life problem.

• Open your books to page 432

Entry Task 03/03/2011

• Get out pg. 435 # 1-8 to check for group points

• Work on your homework and prepare any questions you may have. If you are finished start on pg. 435 #9-17, 34-35.

Entry Task 03/04/2011

• Choose one of the following:– Work on missing work

– Take the Quiz.

• If you are not working you will have to take the quiz.